The invention relates generally to imaging and other systems that process information including phase data, and more specifically to a method and system for three dimensional phase unwrapping for such systems, including particularly various magnetic resonance (MR) applications.
Phase information contained within received signals is used in several imaging applications to produce useful images. Synthetic Aperture Radar systems, for example use several scans from an airplane or a satellite to construct a topographic map of large areas of land. Other imaging applications which use phase based information include MRI, acoustic imaging, interferometry, and X Ray crystallography. Such phase information is also useful in optical Doppler tomography where the phase difference in the two received signals is used to measure the velocity of blood within a tissue.
Another application of phase information is for mapping the static fields required for MR processes. Homogeneous static fields are required for MR processes such as imaging (MRI) and spectroscopy (MRS). MR equipment maps the static field to determine the distribution of inhomogeneities which may then be corrected by using shim coils. Such mapping includes determining and correcting phase jumps in the static field.
One common problem encountered while mapping of fields in MR systems is phase wrapping. Phase wrapping refers to phase values of greater than 2Π or less than zero. It occurs because the measuring system measures values between 0 degrees and 360 degrees (2Π radians) and angles over 2Π are registered as the difference between actual angle and 360 degrees. Thus the measurement of field inhomogeneities results in “phase jumps” when there are phase angles greater than 2Π. Since the system only measures angles between zero and 2Π, a resultant phase angle between zero and 2Π may be “wrapped around” i.e. be a angle greater than 2Π. Determining whether a measured angle is in the range of zero to 2Π, or outside that range, and correcting out-of-range values is called phase unwrapping. Because algebraic manipulations of the phase map require continuity in the phase of measured signal, it is desirable to perform phase unwrapping, such as to correct field inhomogeneities in MR applications.
Currently, phase unwrapping methodologies undertake phase unwrapping in two dimensions only and consist of detecting pixel locations of the phase discontinuities, finding an ordering among pixel locations for unwrapping the phase, and adding offsets of multiples of 2Π. Phase unwrapping in images is often performed by computationally intensive, off-line systems under user guidance.
There is a need in the field for a fast, computationally efficient phase unwrapping methodology in three dimensions for correcting phase jumps for MR and other applications.